【作者】 鲁永红；

【导师】 傅衣铭；

【作者基本信息】 湖南大学 ， 工程力学， 2005， 硕士

【摘要】 综合考虑结构的几何非线性、材料的塑性与粘弹性,以及损伤效应等因素,对纤维增强复合材料板、钢筋混凝土板以及堆石坝进行非线性静、动力学分析,可以更好地揭示结构的力学行为。对其进行研究,不仅具有较高的理论价值,也具有实际的工程应用意义。 本文中,基于Schapery的三维本构关系,采用Kachanov损伤演化方程,构建了考虑基体横向开裂的粘弹性对称正交铺设层合板的本构模型,根据Boltzmann叠加原理和Von Karman非线性板理论,建立了考虑损伤效应的层合板的非线性动力学控制方程;基于不可逆热力学原理,从数学上的不变量出发,建立了一般各向异性弹脆性材料的损伤本构关系及相应的损伤演化方程,根据Von Karman非线性板理论,获得了双参数弹性地基上钢筋混凝土板的非线性静动力控制方程;基于沈珠江的双屈服面模型,采用Merchant流变法则,建立了混凝土面板堆石坝中堆石体的粘塑性本构关系,考虑面板和堆石体间的耦合效应,建立了坝体和面板的非线性控制方程。 在以上工作的基础上,对变量函数在空间上应用有限差分法离散,时间上采用Newmark法离散,整个问题进行迭代求解。具体分析了具损伤复合材料层合板的非线性动力响应、非线性幅频响应以及混沌现象;讨论了损伤对钢筋混凝土结构的非线性静动力响应的影响,数值结果表明,损伤引起结构刚度变化,明显地改变了结构的非线性动力响应;分析了堆石坝中坝体的位移和钢筋混凝土面板的损伤演化过程,绘制了坝体的沉降位移及水平位移的等值线图,可为混凝土面板堆石坝的工程设计提供理论依据。更多还原

【Abstract】 By considering geometric nonlinearity of the structures, plasticity and viscoelasticity of the material, and damage effect synthetically in the process of the nonlinear static and dynamic analysis for composite material plate, reinforced concrete plate and rockfill dam, a better revealment of the mechanics behaviors of these structures will be obtained. Therefore, the research works of them not only have high theory values, but also mean a lot for engineering applications.In this thesis, based on the Schapery’s 3-D constitutive relationship and Kachanov’s damage evolution equations, the constitutive model for viscoelastic symmetric cross-ply laminated plates with transverse matrix crack is founded. Then according to the Boltzmann’s superposition principle and Von Karman’s nonlinear plate theory, the nonlinear dynamic governing equations of the laminated plates considering damage effect are derived. In addition, on the basis of irreversible thermodynamics principle, the damage constitutive relationship and the corresponding damage evolution equations of the anisotropic elastic-brittle materials are established directly from the invariable theory in mathematics. Then according to the Von Karman’s nonlinear plate theory, the nonlinear static and dynamic governing equations of the reinforced concrete plates on the two-parameter foundation are gained. What’s more, base on the Shen’s double yield surfaces model and Merchant’s rheological model, the viscoplastic constitutive equations for the rockfill body of the rockfill dam with reinforced concrete surface are founded. Then, considering the coupling effect of the rockfill and the surface, the nonlinear governing equations are founded.Based on the work above, by using the finite difference method and Newmark scheme, the variable functions are separated and these equations are iterated to seek solutions. The nonlinear dynamic responses, the nonlinear amplitude-frequency responses and the chaotic phenomenon of the laminated plate with damage are analyzed. Furthermore, the effects of damage on the nonlinear static and dynamic response of the reinforced concrete structures are also discussed, the research result of which indicate that the value of stiffness coefficients vary with the damage, which result in the distinct change of the nonlinear dynamic response of the structure. In addition, the displacement of the rockfill body and the damage evolution process of the reinforced concrete surface are analyzed. And the contour charts of the vertical displacement and horizontal displacement are drawn respectively, which may provide更多还原